It's grammatically correct but it's very undiplomatic! We don't tend to comment on other people's weight, particularly when it's a negative observation. I find the use of "fatter" particularly unpleasant. I might be persuaded by "... and noticed that she had put on a lot of weight since they met for the first time". Even then, it's really only acceptable as a report of something he noticed and kept to himself. I sincerely hope he didn't tell Anna or anyone else what he thought.
Student or Learner